A Comparison of Performance Measures for Online Algorithms

Boyar, Joan; Irani, Sandy; Larsen, Kim S.

doi:10.1007/978-3-642-03367-4_11

Cited by 28 publications

(26 citation statements)

References 13 publications

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“…The online search problem does not have partial solutions, so the findings obtained in this paper are complementary to the results obtained in [7].…”

Section: Introductionsupporting

confidence: 72%

“…Not that much is known about the strengths and weaknesses of these alternatives in comparison with each other. In [7], a systematic study of performance measures was initiated by fixing a (simple) online problem and applying a collection of performance measures. Partial conclusions were obtained in demonstrating which measures focus on greediness as an algorithmic quality.…”

Section: Introductionmentioning

confidence: 99%

“…Greediness, as explored in the server problem [7], has to do with focus on which choice to make when advancing from one partial solution to another, closer to the end result. The online search problem does not have partial solutions, so the findings obtained in this paper are complementary to the results obtained in [7].…”

Section: Introductionmentioning

confidence: 99%

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A comparison of performance measures via online search

Boyar

Larsen

Maiti

2014

Theoretical Computer Science

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Though competitive analysis has been a very useful performance measure for the quality of online algorithms, it is recognized that it sometimes fails to distinguish between algorithms of different quality in practice. A number of alternative measures have been proposed, but, with a few exceptions, these have generally been applied only to the online problem they were developed in connection with. Recently, a systematic study of performance measures for online algorithms was initiated [Boyar, Irani, Larsen: Eleventh International Algorithms and Data Structures Symposium 2009], first focusing on a simple server problem. We continue this work by studying a fundamentally different online problem, online search, and the Reservation Price Policies in particular. The purpose of this line of work is to learn more about the applicability of various performance measures in different situations and the properties that the different measures emphasize. We investigate the following analysis techniques: Competitive, Relative Worst Order, Bijective, Average, Relative Interval, Random Order, and Max/Max. In addition to drawing conclusions on this work, we also investigate the measures' sensitivity to integral vs. real-valued domains, and as a part of this work, generalize some of the known performance measures. Finally, we have established the first optimality proof for Relative Interval Analysis.

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“…The online search problem does not have partial solutions, so the findings obtained in this paper are complementary to the results obtained in [7].…”

Section: Introductionsupporting

confidence: 72%

Section: Introductionmentioning

confidence: 99%

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A comparison of performance measures via online search

Boyar

Larsen

Maiti

2014

Theoretical Computer Science

Self Cite

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“…In very recent work Boyar, Irani and Larsen [15] studied the two-server problem on three collinear points under various measures, including bijective analysis. But can the latter be applied successfully into a broader class of problems?…”

Section: Discussionmentioning

confidence: 99%

Paging and list update under bijective analysis

Angelopoulos

Schweitzer

2013

J. ACM

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It has long been known that for the paging problem in its standard form, competitive analysis cannot adequately distinguish algorithms based on their performance: there exists a vast class of algorithms which achieve the same competitive ratio, ranging from extremely naive and inefficient strategies (such as Flush-When-Full), to strategies of excellent performance in practice (such as Least-Recently-Used and some of its variants). A similar situation arises in the list update problem: in particular, under the cost formulation studied by Martínez and Roura [TCS 2000] and Munro [ESA 2000] every list update algorithm has, asymptotically, the same competitive ratio. Several refinements of competitive analysis, as well as alternative performance measures have been introduced in the literature, with varying degrees of success in narrowing this disconnect between theoretical analysis and empirical evaluation.In this paper we study these two fundamental online problems under the framework of bijective analysis [Angelopoulos, López-Ortiz, SODA 2007 and LATIN 2008]. This is an intuitive technique which is based on pairwise comparison of the costs incurred by two algorithms on sets of request sequences of the same size. Coupled with a well-established model of locality of reference due to Albers, Favrholdt and Giel [JCSS 2005], we show that LeastRecently-Used and Move-to-Front are the unique optimal algorithms for paging and list update, respectively. Prior to this work, only measures based on average-cost analysis have separated LRU and MTF from all other algorithms. Given that bijective analysis is a fairly stringent measure (and also subsumes average-cost analysis), we prove that in a strong sense LRU and MTF stand out as the best (deterministic) algorithms.

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“…In very recent work Boyar, Irani and Larsen [11] studied the two-server problem on three collinear points under various measures, including bijective analysis. But can the latter be applied successfully into a broader class of problems?…”

Section: Future Workmentioning

confidence: 99%

Paging and List Update under Bijective Analysis

Angelopoulos¹,

Schweitzer²

2009

Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms

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It has long been known that for the paging problem in its standard form, competitive analysis cannot adequately distinguish algorithms based on their performance: there exists a vast class of algorithms which achieve the same competitive ratio, ranging from extremely naive and inefficient strategies (such as Flush-When-Full), to strategies of excellent performance in practice (such as Least-Recently-Used and some of its variants). A similar situation arises in the list update problem: in particular, under the cost formulation studied by Martínez and Roura [TCS 2000] and Munro [ESA 2000] every list update algorithm has, asymptotically, the same competitive ratio. Several refinements of competitive analysis, as well as alternative performance measures have been introduced in the literature, with varying degrees of success in narrowing this disconnect between theoretical analysis and empirical evaluation.In this paper we study these two fundamental online problems under the framework of bijective analysis López-Ortiz, SODA 2007 and LATIN 2008]. This is an intuitive technique which is based on pairwise comparison of the costs incurred by two algorithms on sets of request sequences of the same size. Coupled with a well-established model of locality of reference due to Albers, Favrholdt and Giel [JCSS 2005], we show that LeastRecently-Used and Move-to-Front are the unique optimal algorithms for paging and list update, respectively. Prior to this work, only measures based on average-cost analysis have separated LRU and MTF from all other algorithms. Given that bijective analysis is a fairly stringent measure (and also subsumes average-cost analysis), we prove that in a strong sense LRU and MTF stand out as the best algorithms.

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A Comparison of Performance Measures for Online Algorithms

Cited by 28 publications

References 13 publications

A comparison of performance measures via online search

A comparison of performance measures via online search

Paging and list update under bijective analysis

Paging and List Update under Bijective Analysis

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